Senate Minority Leader Mitch McConnell restated that vow Friday, saying on the Laura Ingraham radio show that if Romney wins and the GOP gains a majority in the Senate, repealing Obamacare "is the first item on the agenda."

But can they?

If Romney wins the White House, his power to gut or eliminate the law is severely limited without the help of Congress. And with slim odds that the GOP will win a filibuster-proof majority in the Senate, congressional Republicans face a steep climb to repeal the president's signature law.

Such long odds have not deterred the law's opponents, though. After the Supreme Court ruled on the health care law, House Republicans quickly promised that they will once again act to repeal the law in its entirety July 11.

That vote is expected to pass easily, much like when the House first voted for repeal Jan. 19, 2011, approving the measure 245-189. House Republicans have already voted 30 times to disrupt, dismantle, defund and repeal provisions in the health care law. No similar attempts have passed in the Senate.

After Chief Justice John Roberts announced the decision Thursday morning, Mitt Romney rushed to the National Mall, with the Capitol Dome perched over his shoulder, to promise to repeal the law on Day One of a Romney presidency.

"What the court did not do in its last day in session, I will do on my first day if elected president of the United States," Romney pledged. "I will act to repeal Obamacare."

The "act" in Romney's sentence might be the key word. He cannot, as president, use an executive order to single-handedly repeal a law that was passed by Congress and upheld by the Supreme Court. But there are three possible ways Romney could go after the Affordable Care Act using executive power, said Michael Dorf, a constitutional law scholar at Cornell Law School.

First, Romney could direct the departments charged with administering the law to grant the states any and all waivers that were written into the law. Because there aren't many of these waivers and those that do exist don't take effect for years, this method would not disable the law quickly enough to appease the GOP and meet his Day One timeframe.

Second, he could instruct his administration not to enforce the law. This tactic is similar to Obama's decision that his administration would no longer deport undocumented immigrants, "but on steroids," Dorf said.

"It's not that he would be prioritizing one part of the act above another, he would be saying he wouldn't do any of it," Dorf said.

Obama's immigration decision "was at the edge of what a president can do," he added. "What Romney would be proposing to do would go way beyond that."

Romney's third and most "radical" option, Dorf said, would be to assert an independent duty as president to act on his own interpretation of the Constitution, despite the Supreme Court's ruling. Thomas Jefferson was the last president to use this line of reasoning in 1801 when he refused to prosecute people under the Sedition Act, which made it a crime to publish "false, scandalous, and malicious writing" against the government or certain officials.

While this option would be the most effective way to quickly and fully repeal the law, Dorf said, it would be like "playing with fire."

"It is possible he could do it and get away with some of it, but it would be at the cost of sparking a Constitution crisis," Dorf said.

The most likely, and politically feasible, scenario is that Romney will not try to act unilaterally and instead will use his presidential bully pulpit to encourage Congress to repeal the bill.

"He's not a hapless giant by any means," said Stephen Hess, a senior fellow emeritus at the Brookings Institution. "He's more powerful than any other single individual around, but it's a system that doesn't allow him to just go ahead and do away with a major act of Congress."

With 47 Republicans in the Senate and 60 votes required to repeal in the upper chamber, even a great night on Nov. 6, 2012, is unlikely to produce a filibuster-proof GOP Senate majority. When the Senate voted in early 2011 on repeal, the vote failed 47-51. Obviously, it will take convincing some Senate Democrats to cross party lines to repeal the bill in Congress.

If Republicans won a simple majority of 51 seats in the Senate, a more possible scenario, they could attempt to repeal the law using reconciliation, a procedural maneuver that would require a simple majority instead of 60 votes. But this politically toxic long-shot would take time to concoct and would not meet Romney's "first day" timeframe.

Now, repeal has re-emerged as a top campaign issue for congressional Republicans, much like the 2010 midterm elections that swept Rep John. Boehner into the speaker's chair.

"It becomes a huge issue going forward to the election in November," Rep. Steve King, R-Iowa, told ABC on the steps of the court immediately after the decision was announced. "Barack Obama has had this around his neck for two and a half years. It will become an albatross around the neck of Barack Obama walking into November."

Asked why it is necessary for the House to act again on repeal, particularly when there are not enough votes in the Senate to repeal it, Boehner also said the Supreme Court's ruling will only act to strengthen his party's resolve this fall.

"The real outcome of today's decision is to strengthen our resolve to make sure that this law is in fact repealed," Boehner, R-Ohio, said. "We're going to work every single day between now and Election Day, and the American people then will get an opportunity to make their decision on Election Day because elections have consequences. The election in 2008 clearly had a consequence that most Americans disagree with."

After Chief Justice Roberts made it clear that the individual mandate was within Congress's power to tax, Rep. Pete Sessions, the chairman of the National Republican Congressional Campaign committee, said Republicans "will call it what it is" as they work to magnify the Democrats efforts to increase taxes.

"It is a tax," Sessions, R-Texas, told reporters in the Speaker's Lobby during votes this morning. "Obama will be a one-term president as a result of this bill."